热传导界面问题的一种神经网络算法  

A neural network algorithm for the heat conduction interface problems

作　　者：王铸础 谢小平[1] WANG Zhu-Chu;XIE Xiao-Ping(School of Mathematics, Sichuan University, Chengdu 610064, China)

机构地区：[1]四川大学数学学院,成都610064

出　　处：《四川大学学报（自然科学版）》2020年第6期1038-1046,共9页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11771312)。

摘　　要：本文讨论了一种单隐层神经网络算法在数值求解热传导界面问题中的应用.该算法设定含有神经网络函数的近似解满足初边值条件和Dirichlet界面条件,并通过求解由原方程导出的关于神经网络权重的离散优化问题来训练近似解中的神经网络,以使得近似解逼近真解.此外,本文还给出了一种基于随机梯度法思想的类随机梯度法来求解相应的离散优化问题.数值算例验证了算法的有效性.This paper discusses a single hidden layer neural network algorithm for the heat conduction interface problems.The proposed algorithm sets the approximate solution to contain a neural network function and to meet the initial/boundary conditions and the Dirichlet interface condition,and trains the neural network by solving the discrete optimization problem derived from the original system so as to obtain the approximate solution.A new optimization algorithm based on the stochastic gradient method is also given to solve the corresponding discrete optimization problem.Numerical examples are provided to verify the effectiveness of the neural network algorithm.

关 键 词：热传导方程 界面问题 神经网络 随机梯度下降法 

分 类 号：O242.2[理学—计算数学]